Home
Class 12
MATHS
If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, t...

If `cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6,` then the possible values of `n` is/are (a) 3 (b) 2 (c) 4 (d) 8

Text Solution

AI Generated Solution

To solve the inequality \( \cot^{-1}\left(\frac{n^2 - 10n + 21.6}{\pi}\right) > \frac{\pi}{6} \), we will follow these steps: ### Step 1: Understand the Inequality We know that the function \( \cot^{-1}(x) \) is strictly decreasing. Therefore, if \( \cot^{-1}(A) > \cot^{-1}(B) \), then \( A < B \). ### Step 2: Apply the Cotangent Function We can apply the cotangent function to both sides of the inequality: \[ ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible values of z is (are) 3 (b) 2 (c) 4 (d) 8

If cot^(-1)(n/(pi))>(pi)/6, n in N , then the maximum value of n is :

If cot^(-1)(n/(pi))>(pi)/6, n in N , then the maximum value of n is :

If cot^(-1)(n/(pi))lt(pi)/(6),ninN then find the minimum value of n

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) 7 (c) 5 (d) none of these

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n the value of sin^(-1)sin2x is (a) 6-2pi (b) 2pi-6 (c) pi-3 (d) 3-pi

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n the value of sin^(-1)2x is 6-2pi (b) 2pi-6 pi-3 (d) 3-pi

If .^(n)P_(3)+.^(n)C_(n-2)=14n , the value of n is (a) 5 (b) 6 (c) 8 (d) 10

Ifint_(log2)^x(dy)/(sqrt(e^y-1))=pi/6,"then " x " is equal to" (a)4 (b) 1n 8 (c) 1n 4 (d) none of these

If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi is pi/6 (b) pi (c) 0 (d) pi/4